In recent years, there has been increased interest in studying how variations to the classic Hele–Shaw model influence the development of viscous fingering patterns. Many of these studies consider the effect of imposing a time-dependent injection rate, specifically to control or reduce the growth of fingers [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}. Further, much attention has been devoted to manipulating the geometry of the Hele–Shaw cell. One of the earliest examples of this approach is by [8]}, who considered the classic Saffman–Taylor experiment [9]} and linearly tapered the gap between the plates in the direction of the fluid flow. Since this experiment, numerous studies have been performed to give further insight into how the taper angle influences viscous fingering [10]}, [11]}, [12]}, [13]}, [14]}. Other popular physical alterations to the Hele–Shaw cell include uniformly separating the plates in time [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, rotating the entire Hele–Shaw cell at a given angular velocity [21]}, [22]}, [23]}, or replacing one of the plates with an elastic membrane [24]}, [25]}, [26]}, [27]}, [28]}, [29]}, [30]}, [31]}. All of these configurations have been shown to produce patterns distinct from traditional Saffman–Taylor fingering.
